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Joaquin "El Chapo" Guzman has asked to speed up the extradition process, an official says

The expectation is he'll be out of Mexico and in the United States within 3 months, says the source

The notorious drug kingpin has twice escaped Mexican prisons

(CNN)Drug lord Joaquin "El Chapo" Guzman not only wants to be extradited from Mexico to the United States -- he wants to go sooner rather than later.

The defense team for the notorious criminal, and two-time prison escapee, has asked to speed up the process to get him out of Mexican custody and into the hands of U.S. authorities, a senior Mexican law enforcement official told CNN on Wednesday.

While it's not clear where Guzman might end up in the United States (he faces a litany of charges in various cities, like Chicago and New York), the Mexican official predicted he'll be there within the next two to three months.

The same source had said in January that the process would take between six months and a year.

Guzman's push to go to the United States marks a sharp turnaround from what his lawyers said immediately after he was recaptured in January, when they filed an injunction to fight any such request.

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"Mr. Guzman Loera should not be extradited to the United States or any other country," attorney Juan Pablo Badillo said then. "Mexico has just laws that are detailed in the General Constitution of the Republic."

Lawyer: Guzman complained of 'torture'

Right now, Guzman is being held in central Mexico's Altiplano maximum security prison -- the same place from which he escaped July. That was the second time the infamous leader of the Sinaloa drug cartel busted out of jail, the first being in 2001 when he escaped in a laundry cart.

Photos:'El Chapo' in prison

Joaquin "El Chapo" Guzman stands in his cell at the Altiplano Federal Prison in Mexico. Increased security measures are being used by authorities to make sure the cartel kingpin doesn't break out of prison for a third time. His most recent escape came in July, when he got out through a hole in the floor of his cell's shower stall. The images in this gallery were obtained by Mexican journalist Carlos Loret de Mola.

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Photos:'El Chapo' in prison

Military vehicles and canine officers guard the Altiplano prison.

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Photos:'El Chapo' in prison

Guards walk down a hallway of the prison, which has installed 400 new cameras. Authorities hope to add another 600 by April.

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Photos:'El Chapo' in prison

An X-ray machine is guarded at the prison's entrance.

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Photos:'El Chapo' in prison

A body scan machine is also at the front entrance.

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Photos:'El Chapo' in prison

An officer operates the body scan machine.

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Photos:'El Chapo' in prison

An officer at the entrance swabs a visitor to detect explosives.

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Mexican authorities have taken pains to make sure he doesn't get out again, or get too comfortable.

Instead, his attorney alleges, Guzman has been subjected to "physical and mental torture."

"He told me, literally, 'Every two hours, at night, they wake me up to take roll. ... They are turning me into a zombie. They do not let me sleep. All I want is just for them to let me sleep,' " attorney Badillo said.

Still, whatever they are doing with him now, Mexican authorities -- who resisted U.S. attempts to have Guzman extradited -- have signaled they don't want the drug chief around much longer.